Forcing nonperiodicity with a single tile
Publication
, Journal Article
Socolar, JES; Taylor, JM
Published in: The Mathematical Intelligencer
March 2012
An aperiodic prototile is a shape for which infinitely many copies can be arranged to fill Euclidean space completely with no overlaps, but not in a periodic pattern. Tiling theorists refer to such a prototile as an "einstein" (a German pun on "one stone"). The possible existence of an einstein has been pondered ever since Berger's discovery of large set of prototiles that in combination can tile the plane only in a nonperiodic way. In this article we review and clarify some features of a prototile we recently introduced that is an einstein according to a reasonable definition.
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Published In
The Mathematical Intelligencer
DOI
Publication Date
March 2012
Volume
34
Issue
1
Related Subject Headings
- General Mathematics
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences
Citation
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Socolar, J. E. S., & Taylor, J. M. (2012). Forcing nonperiodicity with a single tile. The Mathematical Intelligencer, 34(1). https://doi.org/10.1007/s00283-011-9255-y
Socolar, J. E. S., and J. M. Taylor. “Forcing nonperiodicity with a single tile.” The Mathematical Intelligencer 34, no. 1 (March 2012). https://doi.org/10.1007/s00283-011-9255-y.
Socolar JES, Taylor JM. Forcing nonperiodicity with a single tile. The Mathematical Intelligencer. 2012 Mar;34(1).
Socolar, J. E. S., and J. M. Taylor. “Forcing nonperiodicity with a single tile.” The Mathematical Intelligencer, vol. 34, no. 1, Mar. 2012. Manual, doi:10.1007/s00283-011-9255-y.
Socolar JES, Taylor JM. Forcing nonperiodicity with a single tile. The Mathematical Intelligencer. 2012 Mar;34(1).
Published In
The Mathematical Intelligencer
DOI
Publication Date
March 2012
Volume
34
Issue
1
Related Subject Headings
- General Mathematics
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences